A method of this type is known from DE 197 02 265 Al. In the case of this known method, the mutual welding of the sheet metal strips and the longitudinal cutting of the sheet metal strips, which are welded together, is effected in two successive operational steps. At each welding station, the two sheet metal strips are first of all welded together by means of several laser heads which are arranged next to one another so that said metal strips firstly form flat tubes, which are connected to one another, along the joint welds. At a cutting station assigned to the welding station at a spacing, the sheet metal strips are then separated from one another by means of cutting lasers along the centre of each joint weld. Several flat tubes, which are arranged adjacently and separated from one another by cuts, are thus produced and wound up into cylinders. The cylinders are then delivered to a filling machine where they are cut into lengths by relatively simple machines and spread into can bodies. The technical costs for carrying out this known method are relatively high because separate laser heads are required for welding and for cutting respectively. By adjusting the mutual spacing of the laser heads in the direction of the strip, the width of the flat tubes to be produced can be altered to the respectively desired diameter of the can bodies to be manufactured later therefrom. Provision must be made thereby that the mutual spacing of the welding lasers corresponds absolutely precisely to the mutual spacing of the cutting lasers. In addition, the cutting lasers must be in exact alignment with the welding lasers in the longitudinal direction of the strip since otherwise the cutting lasers do not cut apart the previously produced joint welds exactly in the centre.